Constant as the Northern Star

There are frequent astronomical references in the plays of William Shakespeare (1564?-1616). One famous example is in the tragedy Julius Caesar, written around 1599, where Julius Caesar states,

“I am constant as the northern star,
Of whose true-fix’d and resting quality
There is no fellow in the firmament.”

Little did Shakespeare know that Ejnar Hertzsprung (1873-1967) would discover some 312 years later in 1911 that Polaris, the North Star, actually varies in brightness. Of course, Shakespeare was referring to Polaris’ proximity to the north celestial pole, but there are multiple ironies in that Polaris varies in brightness—albeit a tiny amount—and it will not always be the “pole star”, thanks to the precession of the Earth’s axis.

Polaris is a classical Cepheid pulsating variable star, with a visual magnitude that has historically ranged as much as 1.9 – 2.1 over a period of about 4 days.

At a distance between 426 and 439 ly, Polaris is the nearest and brightest Cepheid variable star in our night sky. Polaris is a supergiant star (F7Ib) weighing in at about 5.4 solar masses. Polaris and its nearest companion star (F6V, 1.3 solar masses) enjoy a complete orbital pas de deux every 30 years.

Currently, Polaris lies only 40 arcminutes from the north celestial pole (declination +89° 20′). As with all stars, the Earth’s rotation causes the stars to wheel around the celestial poles, although in the case of Polaris the angular speed is exceedingly slow, making it a great target for a telescope without a clock drive.

Let’s figure out how fast glacial Polaris moves. It traverses a tiny circle around the north celestial pole every sidereal day (23h56m04s), so what is its angular speed? We need only divide the path length (the circumference of a circle of radius 40′) in arcseconds by the number of seconds in a sidereal day to get the angular speed in arcseconds per second of time. The circumference of a circle is 2πr, so plugging and chugging we get [(2)(3.141592654)(40*60)] / 86164 = 0.18 arcsecond per second of time. Sound like a lot, or a little? This angular speed means that Polaris moves an arcsecond every 5.7 seconds, or 11 arcseconds every minute, or 11 arcminutes every hour. That’s just 4.2° per day.